%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG007-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:26:18 AM UTC 2026
% Result : Unsatisfiable 6.91s 1.33s
% Output : CNFRefutation 6.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of formulae : 65 ( 32 unt; 0 def)
% Number of atoms : 132 ( 10 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 140 ( 73 ~; 67 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 179 ( 0 sgn 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_identity1,axiom,
! [VAR_0] : sum(additive_identity,VAR_0,VAR_0),
file('theBenchmark.p',additive_identity1) ).
cnf(c_1,plain,
sum(additive_identity,A,A),
inference(clausify,[status(thm)],[additive_identity1]) ).
fof(additive_identity2,axiom,
! [VAR_0] : sum(VAR_0,additive_identity,VAR_0),
file('theBenchmark.p',additive_identity2) ).
cnf(c_2,plain,
sum(A,additive_identity,A),
inference(clausify,[status(thm)],[additive_identity2]) ).
fof(closure_of_addition,axiom,
! [VAR_0,VAR_1] : sum(VAR_0,VAR_1,add(VAR_0,VAR_1)),
file('theBenchmark.p',closure_of_addition) ).
cnf(c_4,plain,
sum(A,B,add(A,B)),
inference(clausify,[status(thm)],[closure_of_addition]) ).
fof(left_inverse,axiom,
! [VAR_0] : sum(additive_inverse(VAR_0),VAR_0,additive_identity),
file('theBenchmark.p',left_inverse) ).
cnf(c_5,plain,
sum(additive_inverse(A),A,additive_identity),
inference(clausify,[status(thm)],[left_inverse]) ).
fof(right_inverse,axiom,
! [VAR_0] : sum(VAR_0,additive_inverse(VAR_0),additive_identity),
file('theBenchmark.p',right_inverse) ).
cnf(c_6,plain,
sum(A,additive_inverse(A),additive_identity),
inference(clausify,[status(thm)],[right_inverse]) ).
fof(associativity_of_addition1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( sum(VAR_0,VAR_4,VAR_5)
| ~ sum(VAR_2,VAR_3,VAR_5)
| ~ sum(VAR_1,VAR_3,VAR_4)
| ~ sum(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',associativity_of_addition1) ).
cnf(c_7,plain,
( sum(A,E,F)
| ~ sum(C,D,F)
| ~ sum(B,D,E)
| ~ sum(A,B,C) ),
inference(clausify,[status(thm)],[associativity_of_addition1]) ).
fof(associativity_of_addition2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( sum(VAR_2,VAR_3,VAR_5)
| ~ sum(VAR_0,VAR_4,VAR_5)
| ~ sum(VAR_1,VAR_3,VAR_4)
| ~ sum(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',associativity_of_addition2) ).
cnf(c_8,plain,
( sum(C,D,F)
| ~ sum(A,E,F)
| ~ sum(B,D,E)
| ~ sum(A,B,C) ),
inference(clausify,[status(thm)],[associativity_of_addition2]) ).
fof(commutativity_of_addition,axiom,
! [VAR_0,VAR_1,VAR_2] :
( sum(VAR_1,VAR_0,VAR_2)
| ~ sum(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',commutativity_of_addition) ).
cnf(c_9,plain,
( sum(B,A,C)
| ~ sum(A,B,C) ),
inference(clausify,[status(thm)],[commutativity_of_addition]) ).
fof(distributivity1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6] :
( sum(VAR_2,VAR_4,VAR_6)
| ~ product(VAR_0,VAR_5,VAR_6)
| ~ sum(VAR_1,VAR_3,VAR_5)
| ~ product(VAR_0,VAR_3,VAR_4)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',distributivity1) ).
cnf(c_12,plain,
( sum(C,E,V6)
| ~ product(A,F,V6)
| ~ sum(B,D,F)
| ~ product(A,D,E)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[distributivity1]) ).
fof(distributivity4,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6] :
( product(VAR_5,VAR_1,VAR_6)
| ~ sum(VAR_2,VAR_4,VAR_6)
| ~ sum(VAR_0,VAR_3,VAR_5)
| ~ product(VAR_3,VAR_1,VAR_4)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',distributivity4) ).
cnf(c_15,plain,
( product(F,B,V6)
| ~ sum(C,E,V6)
| ~ sum(A,D,F)
| ~ product(D,B,E)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[distributivity4]) ).
fof(addition_is_well_defined,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_2 = VAR_3
| ~ sum(VAR_0,VAR_1,VAR_3)
| ~ sum(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',addition_is_well_defined) ).
cnf(c_16,plain,
( C = D
| ~ sum(A,B,D)
| ~ sum(A,B,C) ),
inference(clausify,[status(thm)],[addition_is_well_defined]) ).
fof(x_squared_is_x,axiom,
! [VAR_0] : product(VAR_0,VAR_0,VAR_0),
file('theBenchmark.p',x_squared_is_x) ).
cnf(c_18,plain,
product(A,A,A),
inference(clausify,[status(thm)],[x_squared_is_x]) ).
fof(prove_a_plus_a_is_id,axiom,
~ sum(a,a,additive_identity),
file('theBenchmark.p',prove_a_plus_a_is_id) ).
cnf(c_19,plain,
~ sum(a,a,additive_identity),
inference(clausify,[status(thm)],[prove_a_plus_a_is_id]) ).
cnf(c_2401,plain,
( sum(A,C,D)
| ~ sum(additive_identity,B,D)
| ~ sum(additive_inverse(A),B,C) ),
inference(resolve,[status(thm)],[c_7,c_6]) ).
cnf(c_2402,plain,
( sum(A,additive_identity,B)
| ~ sum(additive_identity,additive_inverse(additive_inverse(A)),B) ),
inference(resolve,[status(thm)],[c_2401,c_6]) ).
cnf(c_21,plain,
sum(A,additive_identity,additive_inverse(additive_inverse(A))),
inference(resolve,[status(thm)],[c_2402,c_1]) ).
cnf(c_2403,plain,
( sum(A,C,D)
| ~ sum(additive_identity,B,D)
| ~ sum(additive_inverse(A),B,C) ),
inference(resolve,[status(thm)],[c_7,c_6]) ).
cnf(c_2404,plain,
( sum(C,add(additive_inverse(C),A),B)
| ~ sum(additive_identity,A,B) ),
inference(resolve,[status(thm)],[c_2403,c_4]) ).
cnf(c_26,plain,
sum(A,add(additive_inverse(A),B),B),
inference(resolve,[status(thm)],[c_2404,c_1]) ).
cnf(c_2405,plain,
( sum(add(D,A),B,E)
| ~ sum(D,C,E)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_8,c_4]) ).
cnf(c_2406,plain,
( sum(add(A,additive_inverse(C)),C,B)
| ~ sum(A,additive_identity,B) ),
inference(resolve,[status(thm)],[c_2405,c_5]) ).
cnf(c_74,plain,
sum(add(A,additive_inverse(B)),B,A),
inference(resolve,[status(thm)],[c_2406,c_2]) ).
cnf(c_91,plain,
sum(A,B,add(B,A)),
inference(resolve,[status(thm)],[c_9,c_4]) ).
cnf(c_2407,plain,
( add(A,B) = C
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_16,c_4]) ).
cnf(c_117,plain,
add(A,additive_identity) = A,
inference(resolve,[status(thm)],[c_2407,c_2]) ).
cnf(c_2408,plain,
( add(A,B) = C
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_16,c_4]) ).
cnf(c_118,plain,
add(additive_identity,A) = A,
inference(resolve,[status(thm)],[c_2408,c_1]) ).
cnf(c_2409,plain,
( product(D,B,E)
| ~ sum(B,C,E)
| ~ sum(B,A,D)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_15,c_18]) ).
cnf(c_2410,plain,
( product(B,A,C)
| ~ sum(A,A,C)
| ~ sum(A,A,B) ),
inference(resolve,[status(thm)],[c_2409,c_18]) ).
cnf(c_2411,plain,
( product(add(A,A),A,B)
| ~ sum(A,A,B) ),
inference(resolve,[status(thm)],[c_2410,c_4]) ).
cnf(c_120,plain,
product(add(A,A),A,add(A,A)),
inference(resolve,[status(thm)],[c_2411,c_4]) ).
cnf(c_2412,plain,
( add(A,B) = C
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_16,c_4]) ).
cnf(c_2413,plain,
add(A,additive_identity) = additive_inverse(additive_inverse(A)),
inference(resolve,[status(thm)],[c_2412,c_21]) ).
cnf(c_2414,plain,
A = additive_inverse(additive_inverse(A)),
inference(paramod,[status(thm)],[c_117,c_2413]) ).
cnf(c_178,plain,
additive_inverse(additive_inverse(A)) = A,
inference(copy,[status(thm)],[c_2414]) ).
cnf(c_2415,plain,
( sum(B,C,E)
| ~ sum(A,D,E)
| ~ sum(add(additive_inverse(A),B),C,D) ),
inference(resolve,[status(thm)],[c_8,c_26]) ).
cnf(c_2416,plain,
( sum(B,C,additive_identity)
| ~ sum(add(additive_inverse(additive_inverse(A)),B),C,A) ),
inference(resolve,[status(thm)],[c_2415,c_5]) ).
cnf(c_2417,plain,
~ sum(add(additive_inverse(additive_inverse(A)),a),a,A),
inference(resolve,[status(thm)],[c_2416,c_19]) ).
cnf(c_215,plain,
~ sum(add(A,a),a,A),
inference(paramod,[status(thm)],[c_178,c_2417]) ).
cnf(c_2418,plain,
( sum(add(A,D),B,E)
| ~ sum(D,C,E)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_8,c_91]) ).
cnf(c_2419,plain,
( sum(add(C,A),additive_inverse(C),B)
| ~ sum(A,additive_identity,B) ),
inference(resolve,[status(thm)],[c_2418,c_6]) ).
cnf(c_2420,plain,
sum(add(A,B),additive_inverse(A),add(additive_identity,B)),
inference(resolve,[status(thm)],[c_2419,c_91]) ).
cnf(c_262,plain,
sum(add(A,B),additive_inverse(A),B),
inference(paramod,[status(thm)],[c_118,c_2420]) ).
cnf(c_2421,plain,
( sum(A,C,E)
| ~ sum(D,additive_inverse(B),E)
| ~ sum(A,add(B,C),D) ),
inference(resolve,[status(thm)],[c_7,c_262]) ).
cnf(c_2422,plain,
( sum(A,C,D)
| ~ sum(A,add(B,C),add(D,additive_inverse(additive_inverse(B)))) ),
inference(resolve,[status(thm)],[c_2421,c_74]) ).
cnf(c_2423,plain,
~ sum(add(A,a),add(B,a),add(A,additive_inverse(additive_inverse(B)))),
inference(resolve,[status(thm)],[c_2422,c_215]) ).
cnf(c_1779,plain,
~ sum(add(A,a),add(B,a),add(A,B)),
inference(paramod,[status(thm)],[c_178,c_2423]) ).
cnf(c_2424,plain,
( sum(add(A,A),C,E)
| ~ product(add(A,A),D,E)
| ~ sum(A,B,D)
| ~ product(add(A,A),B,C) ),
inference(resolve,[status(thm)],[c_12,c_120]) ).
cnf(c_2425,plain,
( sum(add(A,A),add(A,A),C)
| ~ product(add(A,A),B,C)
| ~ sum(A,A,B) ),
inference(resolve,[status(thm)],[c_2424,c_120]) ).
cnf(c_2426,plain,
( sum(add(A,A),add(A,A),B)
| ~ product(add(A,A),add(A,A),B) ),
inference(resolve,[status(thm)],[c_2425,c_91]) ).
cnf(c_2399,plain,
sum(add(A,A),add(A,A),add(A,A)),
inference(resolve,[status(thm)],[c_2426,c_18]) ).
cnf(c_2400,plain,
$false,
inference(resolve,[status(thm)],[c_2399,c_1779]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG007-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.38 % Computer : n006.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sat Sep 26 05:44:10 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.38 % Process 499752 was started by sandbox2 on n006,
% 0.10/0.38 % Sat Sep 26 05:44:10 2026
% 0.10/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.39
% 0.10/0.39 % From the command line: assign(max_seconds, 300).
% 6.91/1.33
% 6.91/1.33 % SZS status Unsatisfiable for theBenchmark
% 6.91/1.33
% 6.91/1.33 % Proof 1 at 0.60 (+ 0.22) seconds.
% 6.91/1.33 % Length of proof is 26.
% 6.91/1.33 % Level of proof is 5.
% 6.91/1.33 % Maximum clause weight is 22.000.
% 6.91/1.33 % Given clauses 72.
% 6.91/1.33
% 6.91/1.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------